Rig a rope spanning two objects
One way to do this is to use Constraints and a mesh:

Instead of a curve, use a mesh object made up of two vertices:


Subdivide it with loopcuts (CtrlL) or W&gt; Subdivide.

Hook each end vertex to the corresponding object (or bone) with CtrlH:


Assign a Vertex Group to the end vertices.

Make the line object a Soft Body object and set the vertex group to the end vertices group:


Add a Skin modifier to the line object, and use Vertex scale (CtrlA in edit mode) to scale the size of the hose.

Add a Subsurf or Bevel modifier afterwards to round the hose out.